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diff --git a/TODO b/TODO
--- a/TODO
+++ b/TODO
@@ -1,166 +1,173 @@
/**
@page todolist Project to-do list
LHAPDF6 TODO list
=================
UNVERSIONED
-----------
- **HERA 1.0 and LHeC PDF migration and approval**
Same procedure as for ATLAS and HERA 1.5. Prod Voica for an update.
VERSION 6.2.0
-------------
+- **2014 -> 2016**
+
+
- **Remove remaining Boost dependencies / move to C++11 (AB)**
Only remaining use is multiarray: replace with Martin's array/SSE code
+ Why is there still a boost::bind use in AlphaS_ODE?!
+
+ Add --cxx flag to lhapdf-config: this will include the -std=c++11 or equivalent
+
Check that unique_ptr and shared_ptr semantics (e.g. ptr-populating code) work as intended.
- **New Fortran API**
Surely something nicer than the LHAPDF5 API can be made? Fortran isn't going
away from the the theory world. Suggest prefixing all functions with "lhapdf"
and basing it on the PDFManager, with explicit commands for switching current PDF.
Ideas: uniform "lhapdf_" prefix, require nset and nmem args for *all* commands, i.e. no "current" set slot.
Requests: way to get LHAPDF ID from current set/PDF. Arbitrary PIDs.
- **Provide a single-string-arg version of lookupPDF**
Needs the signature of the function(s) for PDF string decoding to be final
before exposing in the API; it's currently in an anon namespace in Factories.cc.
- **Check LHAGlue getthresholdm_ etc.**
VERSION 6.2.1
-------------
- **Optimize the grid PDF interpolator code**
Cache log(x), log(Q) between samplings -> log() still accounts for 15% of
CPU: can reduce by factor of 13 in some use cases (only one call for a whole
flavour interpolation set at the same point). Below threshold? Sherpa already
report performance increases due to being able to interpolated one flavour at
a time, so perhaps this use case is not valid in all generators and could be
a more complexity than it is worth.
- **Speed up interpolation (MR)**
Many studies already... and Martin has done the important work to de-Boostify
the interpolation grid data objects.
Report of 6.0.4 slowness relative to LHAPDF5 (on CT10). Weird, we tested this
at version 6.0.0 and it was outperforming LHA5. Maybe it is slower for CT10
and ~same for CT10nlo. Juan reports that the NNPDF functions are faster.
Possible speed-ups: caching the last log(x) and log(Q2) values, caching grid
index lookup, caching interpolation weights, using a
native array implementation in place of Boost::multiarray, doing a faster
hybrid search in the grids, GCC builtins for SSE auto-vectorisation.
Martin has got some speed-up out of a native array implementation, and found
no benefit of changing the index search. Andy will look into caching.
- **Add an lhapdf show command**
To print pdfsets.index + cat .info for already installed PDFs.
- **Consider extrapolated cubic splines at subgrid edges (cf. Valerio Berton et al)**
- **Make it possible to find all metadata keys -- both locally and cascaded (AB)**
- **.LHgrid etc. old-name-tolerance control -- TranslateLHA5Names flag?**
VERSION 6.3
-----------
- **Nuclear PDFs**
There's definitely a need for interfaces both to individual nuclear modification
functions (like PDFs themselves, a function of x,Q2) for application on top
of nucleon PDFs, and for all-inclusive nuclear PDFs. Individual "sets" for
each nucleus (A) as well as error sets: need to decide on groupings as well
as the API. Quite active, cf. "Lisbon Accord".
In contact with Hannu. Extend string access syntax to include multiplication
of PDFs e.g. mkPDF("foo/0 * bar"), mkPDF("foo * bar/0"), mkPDF("foo * bar")
returns PDF <- CompositePDF
More general than just nPDFs. Move extended ID string decoding to user-accessible functions.
- **Introduce minimal abstract C++ interface**
Since composite PDFs don't obviously have some current PDF features. Prefer to
re-purpose PDF as the interface than to add a new PDFBase or similar?
AS AND WHEN
-----------
- **Handle zipped PDF .dat files (AB)**
Prefer zipped single member data files rather than virtual filesystem access
to the tarball. Can transparently read zipped files with LD_PRELOAD and
zlibc: is that enough? Or
- **Speed up interpolation with GPUs**
Interpolation of PDFs seems like an potential use case for GPUs, since it's
normal to query for all partons in the set at once: if we can load the
relevant ipol anchors for all flavours onto the GPU then we can maybe get a
substantial speedup. OpenMP did not particuarly help, from quick tests.
- **PDF flavor aliasing mechanism**
e.g. allow anti-flavours to be identical without duplicating their grids in
the data files or memory. How could we implement this?
- **Allow use of valence/sea etc. decompositions?**
GridPDF may be inherited from to allow the returned values to be built from
separate interpolations of component PDFs such as interpolated valence, sea,
or difference PDFs that are combined to make the physical ones. The PDG ID
code range for "generator specific" applications may be used, but we'll need
to bear in mind that this will mean that the flavor ID list has different
meanings and contents for internal and external purposes: maybe the
"internal" PDG ID list needs to become part of the grid data header, or can
the metadata be used?
- **Using std::function to generically modify the interpolation measures in x, Q (AB)**
- **Separate the x and Q2 inter/extrapolation?**
Allow mix & match combinations. Would this simplify the code since the
1D interpolation methods are very simple and the 2D is built from them?
- **Make GridPDFs not read their info or data blocks until an xf value is requested?!**
Super-laziness! But is there a real gain other than < 1 sec initialization speed?
*/
diff --git a/src/AlphaS_ODE.cc b/src/AlphaS_ODE.cc
--- a/src/AlphaS_ODE.cc
+++ b/src/AlphaS_ODE.cc
@@ -1,312 +1,313 @@
// -*- C++ -*-
//
// This file is part of LHAPDF
// Copyright (C) 2012-2014 The LHAPDF collaboration (see AUTHORS for details)
//
#include "LHAPDF/AlphaS.h"
#include "LHAPDF/Utils.h"
#include "boost/bind.hpp"
namespace LHAPDF {
+
// Calculate first order derivative, dy/dt, as it appears in the differential equation
double AlphaS_ODE::_derivative(double t, double y, const vector<double>& beta) const {
if ( _qcdorder == 0 ) return 0;
const double b0 = beta[0];
double d = (b0*y*y);
if ( _qcdorder == 1 ) return - d / t;
const double b1 = beta[1];
d += (b1*y*y*y);
if ( _qcdorder == 2 ) return - d / t;
const double b2 = beta[2];
d += (b2*y*y*y*y);
if ( _qcdorder == 3 ) return - d / t;
const double b3 = beta[3];
d += (b3*y*y*y*y*y);
return - d / t;
}
// Calculate decoupling for transition from num. flavour = ni -> nf
double AlphaS_ODE::_decouple(double y, double t, unsigned int ni, unsigned int nf) const {
if ( ni == nf || _qcdorder == 0 ) return 1.;
double as = y / M_PI;
unsigned int heavyQuark = nf > ni ? nf : ni;
std::map<int, double>::const_iterator quark = _quarkmasses.find(heavyQuark);
if ( quark == _quarkmasses.end() ) throw AlphaSError("Quark masses are not set, required for using the ODE solver with a variable flavor scheme.");
const double qmass = quark->second;
double lnmm = log(t/sqr(qmass));
double as1 = 0, as2 = 0, as3 = 0, as4 = 0;
if ( ni > nf ) {
as1 = - 0.166666*lnmm*as;
as2 = (0.152778 - 0.458333*lnmm + 0.0277778*lnmm*lnmm)*as*as;
as3 = (0.972057 - 0.0846515*nf + (- 1.65799 + 0.116319*nf)*lnmm +
(0.0920139 - 0.0277778*nf)*lnmm*lnmm - 0.00462963*lnmm*lnmm*lnmm)*as*as*as;
as4 = (5.17035 - 1.00993*nf - 0.0219784*nf*nf + (- 8.42914 + 1.30983*nf + 0.0367852*nf*nf)*lnmm +
(0.629919 - 0.143036*nf + 0.00371335*nf*nf)*lnmm*lnmm + (-0.181617 - 0.0244985*nf + 0.00308642*nf*nf)*lnmm*lnmm*lnmm +
0.000771605*lnmm*lnmm*lnmm*lnmm)*as*as*as*as;
} else {
as1 = 0.166667*lnmm*as;
as2 = (- 0.152778 + 0.458333*lnmm + 0.0277778*lnmm*lnmm)*as*as;
as3 = (- 0.972057 + 0.0846515*ni + (1.53067 - 0.116319*ni)*lnmm +
(0.289931 + 0.0277778*ni)*lnmm*lnmm + 0.00462963*lnmm*lnmm*lnmm)*as*as*as;
as4 = (- 5.10032 + 1.00993*ni + 0.0219784*ni*ni + (7.03696 - 1.22518*ni - 0.0367852*ni*ni)*lnmm +
(1.59462 + 0.0267168*ni + 0.00371335*ni*ni)*lnmm*lnmm + (0.280575 + 0.0522762*ni - 0.00308642*ni*ni)*lnmm*lnmm*lnmm +
0.000771605*lnmm*lnmm*lnmm*lnmm)*as*as*as*as;
}
double decoupling = 1.;
decoupling += as1;
if ( _qcdorder == 1 ) return decoupling;
decoupling += as2;
if ( _qcdorder == 2 ) return decoupling;
decoupling += as3;
if ( _qcdorder == 3 ) return decoupling;
decoupling += as4;
return decoupling;
}
// Calculate the next step, using recursion to achieve
// adaptive step size. Passing by reference explained
// below.
void AlphaS_ODE::_rk4(double& t, double& y, double h,
const double allowed_change, const vector<double>& bs) const {
// Determine increments in y based on the slopes of the function at the
// beginning, midpoint, and end of the interval
const double k1 = h * _derivative(t, y, bs);
const double k2 = h * _derivative(t + h/2.0, y + k1/2.0, bs);
const double k3 = h * _derivative(t + h/2.0, y + k2/2.0, bs);
const double k4 = h * _derivative(t + h, y + k3, bs);
const double change = (k1 + 2*k2 + 2*k3 + k4) / 6.0;
// Only call recursively if Q2 > 1 GeV (constant step
// size after this)
if (t > 1. && fabs(change) > allowed_change) {
_rk4(t, y, h/2., allowed_change, bs);
} else {
y += change;
t += h;
}
}
// Solve for alpha_s(q2) using alpha_s = y and Q2 = t as starting points
// Pass y and t by reference and change them to avoid having to
// return them in a container -- bit confusing but should be more
// efficient
void AlphaS_ODE::_solve(double q2, double& t, double& y,
const double& allowed_relative, double h, double accuracy) const {
if ( q2 == t ) return;
while (fabs(q2 - t) > accuracy) {
/// Can make the allowed change smaller as the q2 scale gets greater, does not seem necessary
const double allowed_change = allowed_relative;
/// Mechanism to shrink the steps if accuracy < stepsize and we are close to Q2
if (fabs(h) > accuracy && fabs(q2 - t)/h < 10 && t > 1.) h = accuracy/2.1;
/// Take constant steps for Q2 < 1 GeV
if (fabs(h) > 0.01 && t < 1.) { accuracy = 0.0051; h = 0.01; }
// Check if we are going to run forward or backwards in energy scale towards target Q2.
/// @todo C++11's std::copysign would be perfect here
if ((q2 < t && sgn(h) > 0) || (q2 > t && sgn(h) < 0)) h *= -1;
// Get beta coefficients
const vector<double> bs = _betas(numFlavorsQ2(t));
// Calculate next step
_rk4(t, y, h, allowed_change, bs);
if (y > 2.) { y = std::numeric_limits<double>::max(); break; }
}
}
/// Interpolate to get Alpha_S if the ODE has been solved,
/// otherwise solve ODE from scratch
double AlphaS_ODE::alphasQ2(double q2) const {
// Tabulate ODE solutions for interpolation and return interpolated value
_interpolate();
return _ipol.alphasQ2(q2);
// // Or directly return the ODE result (for testing)
// double h = 2;
// const double allowed_relative = 0.01;
// const double faccuracy = 0.01;
// double accuracy = faccuracy;
// double t = sqr(_mz); // starting point
// double y = _alphas_mz; // starting value
// _solve(q2, t, y, allowed_relative, h, accuracy); // solve ODE
// return y;
}
// Solve the differential equation in alphaS using an implementation of RK4
void AlphaS_ODE::_interpolate() const {
if ( _calculated ) return;
// Initial step size
double h = 2.0;
/// This the the relative error allowed for the adaptive step size.
const double allowed_relative = 0.01;
/// Accuracy of Q2 (error in Q2 within this / 2)
double accuracy = 0.001;
// Run in Q2 using RK4 algorithm until we are within our defined accuracy
double t;
double y;
if (_customref) {
t = sqr(_mreference); // starting point
y = _alphas_reference; // starting value
} else {
t = sqr(_mz); // starting point
y = _alphas_mz; // starting value
}
// If a vector of knots in q2 has been given, solve for those.
// This creates a default grid which should be overkill for most
// purposes
if ( _q2s.empty() ) {
for (int q = 1; (q/10.) < 1; ++q) {
_q2s.push_back(sqr(q/10.));
}
for (int q = 4; (q/4.) < _mz; ++q) {
_q2s.push_back(sqr(q/4.));
}
for (int q = ceil(_mz/4); (4*q) < 1000; ++q) {
_q2s.push_back(sqr(4*q));
}
for (int q = (1000/50); (50*q) < 2000; ++q) {
_q2s.push_back(sqr(50*q));
}
if ( _flavorthresholds.empty() ) {
for (int it = 4; it <= 6; ++it) {
std::map<int, double>::const_iterator element = _quarkmasses.find(it);
if ( element == _quarkmasses.end() ) continue;
_q2s.push_back(sqr(element->second)); _q2s.push_back(sqr(element->second));
}
} else {
for (int it = 4; it <= 6; ++it) {
std::map<int, double>::const_iterator element = _flavorthresholds.find(it);
if ( element == _flavorthresholds.end() ) continue;
_q2s.push_back(sqr(element->second)); _q2s.push_back(sqr(element->second));
}
}
sort(_q2s.begin(),_q2s.end());
}
// If for some reason the highest q2 knot is below m_{Z},
// force a knot there anyway (since we know it, might as well
// use it)
if ( _q2s[_q2s.size()-1] < sqr(_mz) ) _q2s.push_back(sqr(_mz));
// Find the index of the knot right below m_{Z}
unsigned int index_of_mz_lower = 0;
while ( _q2s[index_of_mz_lower + 1] < sqr(_mz) ) {
if ( index_of_mz_lower == _q2s.size() -1 ) break;
index_of_mz_lower++;
}
vector<pair<int, double> > grid; // for storing in correct order
grid.reserve(_q2s.size());
double low_lim = 0;
double last_val = -1;
bool threshold = false;
// We do this by starting from m_{Z}, going down to the lowest q2,
// and then jumping back up to m_{Z} to avoid calculating things twice
for ( int ind = index_of_mz_lower; ind >= 0; --ind) {
const double q2 = _q2s[ind];
// Deal with cases with two identical adjacent points (thresholds) by decreasing step size,
// allowed errors, and accuracy.
if ( ind != 0 && ind != 1 ) {
if ( q2 == _q2s[ind-1] ) {
last_val = q2;
threshold = true;
_solve(q2, t, y, allowed_relative/5, h/5, accuracy/5);
grid.push_back(make_pair(ind, y));
y = y * _decouple(y, t, numFlavorsQ2(_q2s[ind+1]), numFlavorsQ2(_q2s[ind-2]));
// Define divergence after y > 2. -- we have no accuracy after that any way
if ( y > 2. ) { low_lim = q2; }
continue;
}
}
// If q2 is lower than a value that already diverged, it will also diverge
if ( q2 < low_lim ) {
grid.push_back(make_pair(ind, std::numeric_limits<double>::max()));
continue;
// If last point was the same we don't need to recalculate
} else if ( q2 == last_val ) {
grid.push_back(make_pair(ind, y));
continue;
// Else calculate
} else {
last_val = q2;
if ( threshold ) { _solve(q2, t, y, allowed_relative/5, h/5, accuracy/5); threshold = false; }
else { _solve(q2, t, y, allowed_relative, h, accuracy); }
grid.push_back(make_pair(ind, y));
// Define divergence after y > 2. -- we have no accuracy after that any way
if ( y > 2. ) { low_lim = q2; }
}
}
if (_customref) {
t = sqr(_mreference); // starting point
y = _alphas_reference; // starting value
} else {
t = sqr(_mz); // starting point
y = _alphas_mz; // starting value
}
for ( size_t ind = index_of_mz_lower + 1; ind < _q2s.size(); ++ind) {
double q2 = _q2s[ind];
// Deal with cases with two identical adjacent points (thresholds) by decreasing step size,
// allowed errors, and accuracy.
if ( ind != _q2s.size() - 1 && ind != _q2s.size() - 2 ) {
if ( q2 == _q2s[ind+1] ) {
last_val = q2;
_solve(q2, t, y, allowed_relative/5, h/5, accuracy/5);
grid.push_back(make_pair(ind, y));
y = y * _decouple(y, t, numFlavorsQ2(_q2s[ind-1]), numFlavorsQ2(_q2s[ind+2]));
// Define divergence after y > 2. -- we have no accuracy after that any way
if ( y > 2. ) { low_lim = q2; }
continue;
}
}
// If q2 is lower than a value that already diverged, it will also diverge
if ( q2 < low_lim ) {
grid.push_back(make_pair(ind, std::numeric_limits<double>::max()));
continue;
// If last point was the same we don't need to recalculate
} else if ( q2 == last_val ) {
grid.push_back(make_pair(ind, y));
continue;
// Else calculate
} else {
last_val = q2;
_solve(q2, t, y, allowed_relative, h, accuracy);
grid.push_back(make_pair(ind, y));
// Define divergence after y > 2. -- we have no accuracy after that any way
if ( y > 2. ) { low_lim = q2; }
}
}
std::sort(grid.begin(), grid.end(),
boost::bind(&std::pair<int, double>::first, _1) < boost::bind(&std::pair<int, double>::first, _2));
vector<double> alphas;
alphas.reserve(_q2s.size());
for ( size_t x = 0; x < grid.size(); ++x ) {
-// cout << sqrt(_q2s.at(x)) << " " << grid.at(x).second << endl;
+ // cout << sqrt(_q2s.at(x)) << " " << grid.at(x).second << endl;
alphas.push_back(grid.at(x).second);
}
_ipol.setQ2Values(_q2s);
_ipol.setAlphaSValues(alphas);
_calculated = true;
}
}

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